“Philomena” is the story of an Irish woman who searches for the son she was forced to give up for adoption many years before. After years of fruitless inquiring, she teams up with a British journalist and learns the truth about her son and about the system that took him away.

Judi Dench and Steve Coogan in “Philomena.”

Philomena Lee was a “Magadelene,” an unmarried girl who got pregnant and was packed off to a convent to have the baby. Then she had to work in a laundry for three and a half years to pay back the nuns who ran the place. She was forced to acknowledge that the baby would be given up for adoption. Little Anthony was given to an American couple who already had three boys and were looking for a girl, but decided to take him as well because he came right up and embraced the mother. The price: a donation of a thousand Irish pounds each.

The film belongs to Judi Dench, who plays the title character as a ordinary, working-class person, a lover of snacks, brandy, and mass-market novels, but one with a steely determination to find out what happened to her son.

The journalist is Martin Sixsmith, played with understated wit by Steve Coogan, a British comedian not well known in this country. Sixsmith has just been sacked from his job as a government spokesperson and sees Philomena’s story as a way back into journalism.

The search for Anthony takes unexpected turns that Philomena accepts with more grace and sense than expected by the somewhat supercilious Sixsmith. Together they solve the mystery and arrive at closure for Philomena, not to mention a career reboot for Sixsmith.

The film is based on Philomena’s true story, as told by Sixsmith in a book. The real-life Philomena said the film is reasonably true to life, and she is thrilled to be played by Judi Dench.

The book was published during an uproar in Ireland over revelations of abuses in the long-established “Magdalene” system. Coupled with disclosures of sexual abuse by priests, the scandal rocked the Catholic Church in Ireland. The film suggests that the church today is not as rigid and authoritarian as it was fifty years ago (which hardly needs to be said). Nevertheless, the emotional climax is a confrontation, initiated by Sixsmith, between Philomena and an aging nun, Sister Hildegarde, who is just as mean and judgmental as she was in the old days — eager to cast the first stone. Naturally, Philomena’s response is far more Christian than Sister Hildegarde’s.

The film is a civilized little British production in which sex is discussed but not shown, there are no car chases, and nothing gets blown up, so it seems unlikely to get much beyond the arthouse circuit. But Dench and Coogan are worth watching, and the search for Anthony provides enough narrative momentum to keep the film going.